Eigenfunction expansion method for the solution of magneto-thermoelastic problems with thermal relaxation and heat source in three dimensions

The paper deals with the study of the disturbances in an electrically conducting infinite elastic solid permeated by a primary magnetic field containing instantaneous point heat source. The electromagnetic equations of Maxwell and the coupled equations of thermoelasticity have been used. It is assumed that the elastic field under consideration is a homogeneous, orthotropic, electrically as well as thermally conducting one. The fundamental equations of the general three-dimensional problem of magneto-thermoelasticity have been written in the form of an inhomogeneous vector matrix differential equation and solved in the Laplace-Fourier transform-domain by eigenfunction method. Finally, the solution for space-time domain has been made by numerical methods and the graphs for stresses, etc., are drawn.